Analysis of Solid Surface Modification - American Chemical Society

100. 9 0 +. 80 +. 70 +. I Ys (mJ/m 2. ) 6 0. 100. Pretreatment temperature (°C). 1 .... The value of Ys drops significantly from 76 approximately to ...
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Chapter 18

Analysis of Solid Surface

Modification

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Eugène Papirer, Alain Vidal, and Henri Balard Centre de Recherches sur la Physico-Chimie des Surfaces Solides, Centre National de la Recherche Scientifique, 24 avenue du Président Kennedy, 68200 Mulhouse, France Inverse gas chromatography (IGC) is used for the determination of the surface energy characteristics of silicas before and after modification by heat treatment or by grafting onto their surface alkyl, poly(ethylene glycol) and alcohol chains. Because of its high sensitivity, IGC reveals the nature of the grafted molecules, which may then be confirmed by independent methods. The addition of finely divided solids to rubber matrices is commonly practiced to increase the performance and service life of these materials. Indeed, without an active filler, a synthetic elastomer like Styrene Butadiene Rubber (SBR )would not be of much use. For instance, a tire made of pure vulcanized SBR would not last more than a few hundred miles. The introduction of coarse filler particles, such as milled quartz or clays, improves the situation so that the tire lasts thousands of miles. However, using active fillers like special grades of carbon black or silica has produced modern tires that operate satisfactorily for tens of thousands of miles. The reinforcement of rubber by the presence of active fillers is a complex phenomenon that depends on the characteristics of the elastomer network and the properties of the fillers. The influential properties are the particle size, the morphology of particle aggregates, and the surface properties. The role of the geometrical characteristics of the filler is well understood, whereas the significance of the surface properties is more difficult to analyze. This situation stems essentiallyfromthe lack of adequate methods to analyze the surface of such small particles andfromthe fact that fillers differfromeach other and need to be considered individually. It is usually not necessary to change the surface activity of carbon blacks, whereas silicas demand special attention. For instance, it is necessary to treat silica before its use in SBR. Coupling agents like y-mercapto propyl triethoxy silanes allow the formation of strong bonds between silica and the polymer. However, strong chemical bonds are not always desirable. This is typically the case for silica/silicone rubber mixes where strong and unavoidable links lead to a hardening of the mix, which becomes brittle and cannot be reworked. In this case, a surface deactivation treatment of the silica is essential. The examples given above indicate the necessity of having a better understanding of the surface properties of divided solids that have received a surface treatment. The objective of this paper is to demonstrate how advantageous inverse gas chromatography (IGC) is in achieving this goal. 0097-6156/89/0391-0248S06.00/0 • 1989 American Chemical Society

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

Analysis of Solid Surface Modification

18. PAPIRER ET AL.

249

Materials and Methods Silicas produced by two processes have been investigated: three samples are representative of the hydropyrogenation process (Aerosil 130, Aerosil 200 and Aerosil 300 from Degussa and referred to as Silica A130, A200 and A300 ), two samples were prepared by a wet, precipitation process (Z 130 and Z 175 from Rhone Poulenc and referred to as PI and P2). These silicas have surface areas of 130,200, 300,130 and 175 m /g respectively, and have a particle size too small to be used in a IGC experiment. Hence, they were agglomerated in an infrared die, crushed, and sieved (100 to 250 p.m). Approximately 0.5 g of silica were introduced into stainless steel columns 50 cm long and 2.17 mm in diameter. Helium was used as the carrier gas at a flow rate of 20 ml/min. Before each measurement, the columns are conditioned at 150°C for 24 h. Symmetrical retention peaks were observed with alkanes. For other peaks, an integrator was used to determine thefirstorder moment. The silicas were modified by grafting alkyl chains, diols, or poly(ethylene glycols) (PEG). Since the hydroxyl groups of the silica are weakly acidic, the grafting reaction corresponds to an esterification:

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2

S i - O H + ROH

> Si-OR + H 0 2

Since esterification is an equilibrium reaction, the treatment was performed using an excess of alcohol. The grafting of alcohols or diols was performed in an autoclave at 150°C. For PEG, special care was taken to avoid oxidation (outgassing of the silica/PEG mix and treatment under N in a sealed tube at 150°C). In each case, the excess reagent was eh'minated either by heat treatment under vacuum (volatile alcohols and diols), or by solvent extraction (THF) in a Soxhlet extractor. Grafting ratios were calculated either from weight loss of grated silicas when heat treated in air at 750°C or from elemental analysis of the modified silica. The two methods give concordant results. 2

Results and Discussion The surface chemistry of silica is, atfirstsight, relatively simple. Only two types of surface groups are possible: the hydroxyl or silanol groups and the oxygen double bridges or siloxane groups. However, free silanols (either isolated or geminal when two hydroxyls are located on the same silicon atom) and associated silanols (adjacent silanols bridged by H-bonding) have different chemical reactivities resulting in different contributions to the surface properties of the oxide. London Component of the Surface Energy of Heated Treated Silicas. Surface energy is usually considered as the sum of two components: the London component (Ys), stemingfromLondon forces, and the specific component (y| ), originatingfromall other types of forces (polar, H-bonding, metallic, etc). Two methods are commonly used for the measurement of surface energies: wettability and adsorption techniques. Thefirstmethod, wettability, can be evaluatedfromthe contact angle of a drop of liquid deposited on the flat surface of the solid. This method hardly applies to powders like silicas because special care must be taken to control the surface porosity of a silica disk made from compressed silica particles. For a chromatographic silica, Kessaissia et al. (1) determined a Ys value close to 100 mJ/m , whereas the polar component of the surface energy was found to be 46 mJ/m^. Hence, the silica exhibits a large surface energy. The second method of Ys determination is based on the interpretation of adsorption isotherms of either the total isotherm (calculation of the spreading pressure) or the initial or linear part of the isotherm. IGC readily provides the necessary information (2). p

2

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

INVERSE GAS CHROMATOGRAPHY

250

An IGC method for the analysis of divided solids and fibers has been initiated by Gray et al. (2). It is illustrated here by the results obtained from the precipitated silica sample (PI). Injecting a series of n -alkanes at infinite dilution (at the limit of detection by the flame ionization detector) usually results in a linear variation of the logarithm of the net retention volumes (V ) with the number of carbon atoms in the n-alkanes. This is illustrated in Figure 1 for measurements performed between 71 and 130°C. Thermodynamic considerations show that and the standard free energy of adsorption of the alkanes are related by N

AGfl = - R T L n V + B

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N

where B is a constant, depending on the choice of reference states of the alkanes in the gaseous and adsorbed states. Thus, experimental observation allows the calculation of an incremental value corresponding to the A G of adsorption of one - C H - group. Further, when measuring AG n as a function of temperature, A H values are calculated. Assuming that AG R and AH^ vary linearly with the number of carbon atoms, and taking into account the relation of Fowkes ( 4 ) for the calculation of the interaction energy through London forces Gray et al. (2) established the following equation : C H 2

2

A

N.a transforms free energy units into surface energy units, N being Avogadro's number and "a" being the area of an adsorbed - C H 2 - group.y ^is the surface energy of a solid made only of - C H - groups; that is polyethylene (PE). Hence, all terms are either known (N, a, Y C H ) or measurable ( A G C H * ) » P t the quantity of interest: Ys. This method was first applied to follow the surface energy characteristics of silica samples prepared by heating, up 700°C, A200 and P2, that is silicas of different origins but comparable surface areas. Gravimetric measurements of the weight losses during heat treatment indicated a smooth evolution of the weight: silica P2 lost much more water than silica A200. Nevertheless, the y£ measurements via IGC at 60°C indicated (Fig.2) a more complex variation with heat treatment. y|f increases dramatically when increasing the temperature up 500°C and then decreases. Both silicas follow similar trends, but significant differences show up between silicas A200 and P2. Surface silanol content measurements, made either by esteriflcation with C H O H or using alkyl aluminium derivatives, point to a progressive elimination of the hydroxyl groups. However silanol groups (approximately 1.5 group/nm ) are still present despite the 700°C heat treatment. Therefore the variation of y£ cannot be justified only by the total concentration of surface hydroxyl groups. In fact Maciel et al. (5.) have shown using solid state NMR that variation of total silanol and geminal silanol contents are not at all connected. The fraction of gerninal silanol groups changes during heat treatment in the same complex way as do y| values. The change in ys values of silica heated above 500°C is possibily related to reorganization ability of silica surface ( £ ) . Indeed, at temperatures above 500°C, sufficient thermal energy is provided to the silica network to allow relaxation of the highest strained siloxane bridges created by condensation of the silanol groups below 500°C.This relaxation is accompanied by variations in surface properties of silicas as demonstrated by IGC.Finally, it is seen that even though IGC is not able to reveal CH

2

e x c e

2

14

3

2

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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18.

PAPIRER ET AL.

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Analysis of Solid Surface Modification

A G £ (kJ/mol)

71.1°C

30 4' ( - R T L n V n + B)

90.7°C

20 4

104

10

8

Figure 1. Variation of the net retention volume (V ) of n-alkanes with number of carbon atoms, measured at different temperatures (column containing precipitated silica PI). N

100

I Ys (mJ/m

2

)

9 0 +

80 +

70 +

Pretreatment 6 0 100

200

300

temperature (°C)

1

1

1

400

500

600

1 — 700

Figure 2. Variation of the London Component (y|) of precipitated (P) and fumed (A 200) silicas upon heat treatment

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

252

INVERSE GAS CHROMATOGRAPHY

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the exact mechanisms of the chemical surface processes induced by thermal treatment, it appears as a most sensitive method to detect changes in the surface properties which are associated with these processes. London Component of the Surface Energy of Silicas Having Alkvl Grafts.Some results pertaining to samples obtained by esterification of silica PI are presented as an example in Figure 3.The data indicate that for these samples, the linear relationship between AG° and AH is accurate.Consequendy, the Ys values may be determinated according to the method oudined earlier. Table I compares the Ys of silicas before and after esterification either with short chains (methyl: C\) or long chains (hexadecyl: CIG), A and P corresponding to the fumed( A130) and precipitated (PI) silicas, respectively. Table I:

London Component of the Surface Energy of Silica (PI and A130) Before and After Methyl (Cj) and Hexadecyl (C^) Esterification p

Chains nm 2

yk (mJ/m2)

98

PC!

PC16

A

ACi

ACi

10.5

2.2

-

3.4

1.5

87

47

75

70

38

PE

6

35-40

The reaction with CH OH also allows the measurement of the silanol amounts. Silicas P and A have different contents. In fact, the content of P is so great that it exceeds the optimum surface coverage capacity (monolayer of - OCH groups). Two hypothesis may be proposed to explain this result. Either the surface of the P silica is rugged, or non-condensed polysilicic acids chains are still present on silica P. Such pendant chains could react efficiently with methanol indicating an apparent excessive value of silanol surface coverage. Grafting methyl chains onto the silicas decreased only slightly the Y£ values, a result accounted for by the small size of the - C H group, which is unable to screen efficiently the silica surface. However, when attaching longer alkyl chains, Ys is greatly decreased and approaches values close to that of polyethylene. An interesting observation can be made when studying silica (A 130) samples modified by grafting alkyl chains of increasing number of C atoms (Figure 4). A striking variation of Ys is recorded with grafts having 7 or 11 carbon atoms. These results are beyond experimental errors, since the Ys measurement is reproducible to within ± 0.5 mJ/m . In Figure 5, Ys is plotted against the number of - C H - groups per unit surface area (nm ). The minima now correspond to approximately 15 CH /nm and 23 CH /nm . Taking 0.06 nm as the mean area of a - C H - groups, it becomes obvious that minima are observed when the surface is covered by one and two monolayers of - C H - groups, respectively. Cross polarization, magic angle spinning solid state C NMR measurements were performed (7) on the series of samples, examining more precisely the mobility of the end methyl group of the alkyl graft. NMR indicates that the mobility of this group is most restrained when either the monolayer or the second layer of -CH - groups are completed on the silica surface. These results suggest that on silica A130, the grafted alkyl chains organize themselves so as to form a dense and regular array of -CH - groups having optimum interaction capacity both with the silioca surface and with neighbouring - C H 3

3

3

2

2

2

2

2

2

2

2

2

2

1 3

2

2

2

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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Analysis of SoliJ Surface Modification

100 AH

A

(kJ/mol)

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80 -

P

60 -

40

»C

'/T

i e

20 AG° (kJ/mol) 0 0

»— 5

10

1

1

1

15

20

25

30

Figure 3. Relation between AH° and AG° of adsorption of n-alkanes on precipitated silicas (PI), methylated (PCj) and hexadecylated (PC ) silica samples. 16

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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INVERSE GAS CHROMATOGRAPHY

groups. Clearly then, under these conditions, the interaction potential of the grafted chains with alkanes, used for IGC, are also reduced. Thus the observed minima in y|f values are explainable. London Component of the Surface Energy of Silicas Modified with Diols. These samples were prepared to compare alkyl grafts, formed during the reaction of silica with alcohols, and similar grafts having a hydroxyl group at their free end. Figure 6 agrees with the results exhibited in Figure 5; that is, Ys passes through a minimum value when a monolayer of - C H - groups is completed on the silica surface. The second rriinimum, approximately at 26-CH -/nm » is less obvious than the previous one. This result is explained by the same considerations as those presented for silicas having alkyl grafts, considerations which also supported by NMR measurements

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2

2

2

London Component of the Surface Energy of Silicas Having PEG Grafts. The dependence of the surface properties of grafted silica on the number of monomer units is also evidenced with silicas (A300) having poly(ethylene glycol) chains attached. Table H presents the y£ values, measured by IGC at 60°C. The other quantities listed are: the molecular weight (Mw) of PEG graft; T, the grafting ratio (weight percent of PEG on silica); and nj^U» the number of monomer units per unit surface area (nm ). 2

Table n: y£ Values Measured at 60°C on Silica A 300 Modified by Grafting of PEG Mw

Y J (mJ/m ) 2

0 2,000 4,000 2,000 2,000 2,000 10,000 4,000 10,000

0 5 7 17 23 56 57 72 75

76 43 36 38 36 30 30 30 32

n

MU

0 2.6 3.7 8.9 12.1 29.5 30.0 37.9 39.5

The value of Ys drops significantly from 76 approximately to 30 to 38 mJ/m when going from the untreated silica to a sample modified by 7 % PEG having a molecular weight of 4.000. This amount corresponds to 3.7 monomer units (- C H C H - O -) nm ; that is, a value sufficient to form a monolayer. A limit value of 30 mJ/m is reached for higher surface coverage. Hence the pertinent factor, when considering grafting PEG onto silica is, not the molecular weight of the graft but rather, as previously outlined with the alkyl grafts, the surface coverage by the monomer units. 2

2

2

2

2

Specific Component of the Surface Energy of Silica having Alkvl Grafts. So far, the focus has been on measuring the y£ values of silicas by IGC. The remainder part of this paper is devoted to the determination of the specific component of the surface energy. A simple method for the determination of the specific component of the surface energy, starting from IGC results, does not exist. However, several attemps have been made (&,9,10 ) to evaluate, through IGC, specific interaction parameters of polar probes with polar surfaces.

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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Analysis of Solid Surface Modification

Figure 5. Variation of y£ with the number of - C H - groups/nm grafted on the surface of Aerosil 130 using alcohols as reactants. 2

2

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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INVERSE GAS CHROMATOGRAPHY

For instance, a possible method to evaluate the contribution of specific interactions consists of the comparison of the chromatographic behaviour of two solutes having similar sizes (cyclohexane and benzene), yet differerg interaction capacities. Figure 7 illustrates this concept where the difference in AG q of benzene and cyclohexane are plotted for three silica (PI) samples at various temperatures. The reference state of the adsorbed molecules is the same as that used by de Boer (11). As expected, the difference is greatest with the untreated silica. Yet, on PC 15, there persists a small possibility of specific interactions. The previous method is essentially qualitative and does not allow prediction of the specific interaction potential of the silicas with other solutes. For a more quantitative approach, a semi-empiric method was developed to extract from the single chromatographic peak (or AG £ ) : the contribution of either London or specific interactions to the net retention volume V . The proposed method is illustrated by the following three figures corresponding respectivily to silica PI and PI samples having methyl and hexadecyl grafts. The first figure relates AG £ to the vapor pressure of the injected solutes (Figure 8). This variable was chosen because it is pertinent thermodynamically. All n-alkane probes define a single straight line. By definition, the deviation from this line is taken as an estimation of the specific interaction parameter I p. A comparison of Figures 8 and 9 does not indicate any major differences, which confirms the fact that the methyl graft is too small in size to shield the silica surface. However, an examination of the results in Figure 10 shows significant differences, since die points corresponding to polar probes are close to the alkane line. When comparing with the results obtained with hexadecylated silica A130 a major difference in behaviour is noted. For silica A C , all experimental points fit this alkane line. This result, reinforced by others (2,11) using techniques such as NMR and IR, is explained by assuming that the alkyl chains on A and P silicas are distributed differently. A regular array, which restricts the approach of the polar solutes to the solid's surface, is postulated for silica A. A patchwork type of organization, which allows polar parts of the surface access to the polar solutes, is postulated for silica P. N

S

16

Specific Component of the Surface Energy of Silicas having PEG Grafts It is possible to take a step further for a more quantitative description of the specific interactions, a solid and a polar probe are able to exchange. It is based on the use of acid/base scales and an equation, which has been proposed earlier by Saint-Flour and Papirer (9) I

sp

= (AN)C + (DN) C ,

where I is the specific energy of interaction defined earlier, (AN) and (DN) are the acceptor and donor number of the probes injected in the GC, and C and C are the capacities of the solid to exchange base or acid type of interactions. When applied for example to PEG grafted silica, this concept demonstrates the influence of the grafting ratio on the surface properties of grafted silica. Initially acidic, the silica acquires more base-like character (due to the ether links of PEG) as the grafting ratio is increased( 12). The results of IGC presented so far demonstrate its ability to determine and evidence minor changes in surfaces properties of solids submitted to various treatments. The last section of this paper will show the potential of IGC for the detection of unexpected molecular arrangements of the grafts on the silica surface. sp

Enthalpies of Interaction of Polar Probes with Silicas modified with Diols. Whereas the treatment of silicas with alcohols leads to fixation of alkyl grafts, their modification with diols results in the grafting of hydrocarbon chains still having a

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

A ( A G

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8 --. •"

257

Analysis of Solid Surface Modification

18. PAPIRER ET AL.

)

A B-cH

( k J / m 0 , )

• T

. '



o

.

60

P

< -

2__JPC1_^

o

1

U

80

100

120

Figure 7. Comparison between the free energies of adsorption of benzene and cyclohexane on precipitated silice (PI), methylated (PCi), and hexadecylated (PCig) silica samples.

A

(kJ/mol)

THF^

Acetone o

Xylene

30-

Ether O

Toluene

20 -

'1 0

sp

CH C 2

C 10-

— C

6

H

°

C

H

C

I

3

2

°

12 ° 6 "5

log P 2.0

1

1

2.5

3.0

0

1

3.5

4.0

Figure 8. Variation of AG j? with logarithm of vapor pressure P of probes (silica PI). G

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

258

INVERSE GAS CHROMATOGRAPHY

40

T

A G ^ (kJ/mol)

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30 -

EtCN O

EtAc Acetone O o THF Ether O 0

Xylene

20

Benzene "1 o CCI

C

4

o

H C I

3

C

g2

C I

2

10

. O r 12

6

log

P

0

2.0 2.5 3.0 3.5 4.0 Figure 9. Variation of AG § with logarithm of vapor pressure P of probes (methylated silica PI). Q

40 AG£ (kJ/mol)

EtCN O

30 EtAc O

20

Acetone *

o

THF

Ether

CHCU

CH^CI 2 2

10 6 1

2.0

2.5

1

3.0

12

log

P

G

1

3.5

4.0

Figure 10. Variation of AG § with logarithm of vapor pressure P of probes (hexadecylated silica PI). Q

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

Analysis of Solid Surf ace Modification

259

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18. PAPIRER ET AL.

Figure 12. Schematic representation of the position of grafted diol chain on a flat silica surface.

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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260

INVERSE GAS CHROMATOGRAPHY

terminal hydroxyl group. Hence, silica samples with different adsorption properties are possibily obtained and the study of their interaction capacity with hydrogene bonding probes should be most appropriate to evidence such differences. Considering closely (Figure 11) the variation of the enthalpies of adsorption of alcohol probes on the surface of silica A130, which has been modified with diols of increasing chain length, a striking observation is made that seems to be related to the number of carbon atoms in the grafted diol. An explanation is proposed in Figure 12 which compares, in a schematic way, the configuration of grafted odd and even diol chains. Several hypotheses are made: - the surface of the silica is planar, on the molecular level; - a diesterification is possible; and - chains adopt a trans-trans configuration. With these hypotheses, it is possible to understand the preferential diesterification reaction that occurs with diols having an odd number of carbons, since the terminal hydroxyl group of the odd diol is in a most favourable position. In fact NMR measurements (7 ) support the preferentiel diesterification reaction when using odd diols. The necessity of considering a flat surface is also demonstrated when comparing the results given by silicas A 130 and PI. Indeed, silica P has a more irregular surface, as can be shown by independent methods ( H ). Finally, the variations illustrated by Figure 11 are not observed with silica PI. Moreover for PI, NMR indicates essentially diesterification . All these facts are in favour of the proposed model. According to this model, the variation of AH on mono and diesterified silica surfaces is accounted for by the greater capacity for H-bonding on the diesterified sample. On a mono-esterified silica, H-bonds already exists between the silanol and the terminal hydroxyl of the graft and does not facilitate the interaction with the alcohol probes. Conclusion IGC appears to be a useful and powerful method for the characterization of divided or fibrous solid surfaces. Because of its extreme sensitivity to small variations in the surface properties of the solid, IGC reveals interesting phenomena to be eventually confirmed by independent analytical methods. This study shows that small and well defined molecules behave in a complex manner when chemically linked to the surface of a solid. Their behaviour is strongly dependent on the characteristics of the graft and the surface, and on geometrical factors like the fractality of the surface. Obviously, the grafting ratio, which determines the intensity of interactions that adjacent grafted molecules experience is also important. It can be expected that the behaviour of a grafted macromolecule will be more complex to analyze. In addition to the aspects considered in this paper, one has to take into account the eventual modifications of the dynamics of the chains located above the polymer layer that is in direct contact with the solid. Acknowledgment The authors thank Miss Clara C. Pizafia for her kind and efficient assistance during the text editing. Literature Cited 1. 2.

Kessaissia, Z.; Papirer, E.; Donnet, J.B. J. Colloid Interface Sci. 1981, 79 (1), 257-63. Conder, J.R.; Young, C.L. In Physicochemical Measurements by Gas Chromatography. John Wiley: New York, 1979.

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

18. PAPIRER ET AL.

3. 4. 5. 6. 7.

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8. 9. 10 11. 12. 13.

Analysis of Solid Surface Modification

Dorris, G.M.; Gray, D.G. J. Colloid Interface Sci. 1980, 77 (2), 353-62. Fowkes,F.M. J. Colloid Interface Sci. 1968, 28 ,493. Sindorf, D.W.; Maciel, G.E. J. Am. Chem. Soc. 1983, 105,1487-1493. Brinker, C.J.; Kirkpatrick, R.J.; Tallant, D.R.; Bunker, B.C.; Montez, B. J.Non-Cryst.Solids 1988, 99, 418-428. Tuel, A.; Hommel, H.; Legrand, A.P.; Balard, H.; Sidqi, M.; Papirer, E. submitted to Chromatographia. Schreiber, H.P.; Richard, C.; Wertheimer, M.R. In Physicochemical Aspects of Polymer Surfaces: Mittal, K.L., Ed.; Plenum Publ. Co.: New York; Vol 2, p 739. Saint Flour, C.; Papirer, E. Ind. Engn. Chem. (Prod. Res. Dev.) 1982, 21 (4), 666-70. Schultz, J.; Lavielle, L.;: This volume. De Boer, H.J. The Dynamical Character of Adsorption. Oxford University Press: London, 1953. Papirer, E.; Balard, H.; Rahmani, Y.; Legrand, A.P.; Facchini, L.;Hommel, H. Chromatographia 1987, 23 (9), 639-647. Zaborski, M.; Vidal, A.; Papirer, E.; Morawski, J.C. submitted to Makromol. Chem.

R E C E I V E D September29,1988

In Inverse Gas Chromatography; Lloyd, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

261